Efficient learning of $t$-doped stabilizer states with single-copy measurements
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909104381886464 |
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| author | Chia, Nai-Hui Lai, Ching-Yi Lin, Han-Hsuan |
| author_facet | Chia, Nai-Hui Lai, Ching-Yi Lin, Han-Hsuan |
| contents | One of the primary objectives in the field of quantum state learning is to develop algorithms that are time-efficient for learning states generated from quantum circuits. Earlier investigations have demonstrated time-efficient algorithms for states generated from Clifford circuits with at most $\log(n)$ non-Clifford gates. However, these algorithms necessitate multi-copy measurements, posing implementation challenges in the near term due to the requisite quantum memory. On the contrary, using solely single-qubit measurements in the computational basis is insufficient in learning even the output distribution of a Clifford circuit with one additional $T$ gate under reasonable post-quantum cryptographic assumptions. In this work, we introduce an efficient quantum algorithm that employs only nonadaptive single-copy measurement to learn states produced by Clifford circuits with a maximum of $O(\log n)$ non-Clifford gates, filling a gap between the previous positive and negative results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_07014 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Efficient learning of $t$-doped stabilizer states with single-copy measurements Chia, Nai-Hui Lai, Ching-Yi Lin, Han-Hsuan Quantum Physics One of the primary objectives in the field of quantum state learning is to develop algorithms that are time-efficient for learning states generated from quantum circuits. Earlier investigations have demonstrated time-efficient algorithms for states generated from Clifford circuits with at most $\log(n)$ non-Clifford gates. However, these algorithms necessitate multi-copy measurements, posing implementation challenges in the near term due to the requisite quantum memory. On the contrary, using solely single-qubit measurements in the computational basis is insufficient in learning even the output distribution of a Clifford circuit with one additional $T$ gate under reasonable post-quantum cryptographic assumptions. In this work, we introduce an efficient quantum algorithm that employs only nonadaptive single-copy measurement to learn states produced by Clifford circuits with a maximum of $O(\log n)$ non-Clifford gates, filling a gap between the previous positive and negative results. |
| title | Efficient learning of $t$-doped stabilizer states with single-copy measurements |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2308.07014 |